Question

A card is drawn at random from a pack of 52 cards, Find the probability that the card drawn is neither a king nor a queen

Two dice are thrown simultaneously. Find the probability of getting a multiple of 3 as the sum.


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Answer 1

For 1st Question :

Given :

• A pack of 52 cards are well shuffled .

To Find :

• Probability of getting a card which is neither a king nor a queen.

Solution :

$\longmapsto\tt{Total\:Cards=52}$

$\longmapsto\tt{Total\:Cards-No.\:of\:queen-No.\:of\:King}$

$\longmapsto\tt{52-4-4}$

$\longmapsto\tt\bf{44}$

$\longmapsto\tt{Fav.\:Outcomes=44}$

$\longmapsto\tt\bf{Probability=\frac{No.\:of\:fav.\:Outcomes}{Total\:No.\:of\:Outcomes}}$

$\longmapsto\tt{\cancel\dfrac{44}{52}}$

$\longmapsto\tt\bf{\dfrac{11}{13}}$

So , The probability of getting a card which is neither a king nor a queen is 11/13...

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For 2nd Question :

Given :

• Two dice are rolled simultaneously.

To Find :

• Probability of getting a multiple of 3 as the sum.

Solution :

$\longmapsto\tt{Total\:Outcomes=36}$

$\longmapsto\tt{Favourable\:Outcomes=12}$

(2,1) (5,1) (2,1) (2,4) (3,3) (3,6) (4,2) (4,5) (5,1) (5,4) (6,3) (6,6)

$\longmapsto\tt\bf{Probability=\frac{No.\:of\:fav.\:Outcomes}{Total\:No.\:of\:Outcomes}}$

$\longmapsto\tt{\cancel\dfrac{12}{36}}$

$\longmapsto\tt\bf{\dfrac{1}{4}}$

So , The probability of getting a multiple of 3 as a sum is 1/4...